George F. Pinder

An experimental study of complete dissolution of a nonaqueous phase liquid in saturated porous media

The attenuation of gamma radiation was utilized to measure changing residual trichloroethylene (TCE) saturation in an otherwise water-saturated porous medium as clean water was flushed through the medium. A front over which dissolution actively occurred was observed. Once developed, this front varied in length from ≈11 mm to ≈21 mm, lengthening as it moved through the porous medium. Gamma attenuation measurements and analyses of effluent water samples indicate that there was minimal if any transport of TCE as colloidal droplets. Even as trapped TCE ganglia decreased in size due to dissolution, there is no evidence that they became mobile and advected downgradient. An extraction of the porous medium at the completion of one experiment indicated that less than 0.002% of the original TCE mass remained, suggesting that minimal amounts of separate phase TCE remained trapped within the medium after flushing with 290 pore volumes. Mass transfer rate coefficients were computed and are shown to be a function of Darcy flux, TCE volumetric content, and distance into the region of residual TCE.

Computational methods in water resources X

1. Groundwater and Flow in Porous Media. 2. Subsurface Transport. 3. Scaling and Heterogeneity. 4. Geostatistics. 5. Reactive Flow. 6. Fractured Porous Media. 7. Parameter Estimation. 8. Remediation and Optimization. 9. Subsurface Multiphase Flow. 10. Saltwater Intrusion. 11. Shallow Water Equations. 12. Flow and Transport in Rivers. 13. Navier--Stokes Equations. 14. Coastal Flow. 15. Sediment Transport. 16. Algebraic Methods. 17. Software Development. 18. Parallel Methods.

Groundwater management using numerical simulation and the outer approximation method for global optimization

Groundwater quantity management problems with fixed charges have been formulated in the past as mixed integer and linear programming problems. In this paper a new methodology is presented where the fixed charges are incorporated into the objective function in an exponential form and the problem is solved as a concave minimization problem. The principal difficulty in the minimization of a concave function over a linear or nonlinear set of constraints is that the local minima which are determined by the classical minimization algorithms may not be global. In an effort to circumvent this problem the outer approximation method is introduced. This method is applicable to the global minimization of a concave function over a compact set of constraints. In the present work the outer approximation is applied to concave minimization problems over a convex compact set of constraints. Two applications of the method to groundwater management problems are presented herein, and the results are compared with an existing solution obtained using a different optimization approach.

Vertical and horizontal land deformation in a desaturating porous medium

Abstract Soil deformation due to the flow of two immiscible fluids can be described by a general three-dimensional deformation field coupled with a three-dimensional hydrologic flow field. The resulting system of equations provides the components of displacement, the pressure and the fluid saturations. The equations governing saturated-unsaturated soil deformation are obtained as a simplified subset of a more general multiphase formulation. These equations can be solved numerically using an iterative Galerkin finite element technique with a weighted implicit finite difference approximation of the time derivative. A mixed stress-displacement formulation of the governing equations provides the flexibility necessary to consider both stress and displacement boundary conditions. The model predicts the commonly ignored horizontal displacements in a variably saturated system undergoing simultaneous desaturation and deformation. This is accomplished using completely coupled stress and pressure fields. The model provides vertical and horizontal displacement and changes in pressure (head) and saturation as a result of fluid withdrawal in a phreatic aquifer.

Simulation of groundwater flow and mass transport under uncertainty

Abstract An analytical tool which facilitates the analysis of stochastic groundwater problems without resorting to Monte Carlo analysis can be developed using an approach analogous to that used in the field of applied mathematics to investigate the propagation of waves in random media. The fundamental assumption of this approach is that the random part of the porous medium property is small compared to the non-random part. This assumption allows us to treat the problem of solving a partial differential equation with stochastic coefficients using perturbation theory.

Designing optimal strategies for contaminated groundwater remediation

Abstract The problem of locating pumps and setting pump rates to most effectively stabilize and remove a plume of contaminated groundwater at a hazardous waste site is examined. Nonlinear optimization methods are combined with convective-disperisve transport simulation in a unit response matrix type of optimization formulation. Constraints are used which guarantee that the contaminant plume is removed by limiting the concentrations at nodal points in the domain at a future time. Additional constraints explicitly require that concentrations not increase in the area outside the initial plume boundary. The effectiveness of alternative formulations are examined by performing numerical experiments using a hypothetical aquifer. The experiments show that computational costs are dominated by the repeated simulations required for computation of constraint gradients and are proportional to the number of pump sites under consideration. This characteristic of the formulation and algorithm used, limits the use of the approach to problems where the number of potential pump sites is relatively small.

Direct measurement of interstitial velocity field variations in a porous medium using fluorescent-particle image velocimetry

Abstract Fluorescent-particle image velocimetry (FPIV) is used in conjunction with refractive-index matching to measure flow velocities in the interstitial regions of a porous medium. Adaptations that allow the use of conventional PIV methodology in index-matched systems are discussed, and the results of flow field measurements in a porous test bed under saturated flow conditions are presented. Preliminary analysis of these data, in which the horizontal and vertical components of the interstitial velocity vectors were averaged over a specified region within the medium, are also presented and compared with the vertical velocity component calculated from the total volumetric flow rate. The magnitude of the macroscopically derived and FPIV-measured values are found to be very similar. In general, our results demonstrate the utility of the FPIV technique to determine both the point velocity and the local volume-averaged velocity within porous media.

Optimal data acquisition strategy for the development of a transport model for groundwater remediation

The reliability of groundwater quality management algorithms is limited in large part by the uncertainty present in the model parameters. Because the field parameter measurement costs and the remediation costs must be supplied by the same financial source, the classical optimization procedure does not minimize the real total remediation investment. This research presents an algorithm able to find the total minimum for the sum of both the measurement and the pumping costs. A chance-constrained technique is used to cast the optimization problem in stochastic form, relating the concentration covariance matrix to the log-transmissivity covariance matrix by means of the transport equations and a first-order approximation for the uncertainty. The simulation model solves the steady state flow equations on a finite element triangular mesh and the transport equations using the backward method of characteristics. The resulting nonlinearly constrained optimization problem is solved using the quasi-linearity algorithm; this algorithm is designed to find a good initial point for the local minimum search when the feasible domain is not convex.

Numerical modeling in science and engineering

Basic Equations of Macroscopic Systems. Introduction to Numerical Methods. Steady-state Systems. Dissipative Systems. Nondissipative Systems. High-order, Nonlinear, and Coupled Systems. Appendix: Summary of Vector and Tensor Analysis. Index.

Orthogonal collocation and alternating-direction procedures for unsaturated flow problems

Abstract The alternating-direction collocation method has recently been developed for general parabolic equations. In order to test the applicability of the procedure to highly nonlinear problems, an alternating-direction collocation algorithm is developed to simulate two-dimensional flow in unsaturated porous media. The algorithm employs an alternating-direction solution procedure within the framework of a modified Picard iteration scheme. Numerical behaviour of the new procedure is compared to the behaviour of a standard two-dimensional collocation formulation. The new method is also tested on several infiltration problems of practical interest, including a layered and sloping soil. Results demonstrate the method to be accurate and highly mass conservative. The algorithm also produces significant savings in both execution time and storage.